impls/composite/composite.c

/*
      Defines a preconditioner that can consist of a collection of PCs
*/
#include <petsc/private/pcimpl.h>
#include <petscksp.h> /*I "petscksp.h" I*/

typedef struct _PC_CompositeLink *PC_CompositeLink;
struct _PC_CompositeLink {
  PC               pc;
  PC_CompositeLink next;
  PC_CompositeLink previous;
};

typedef struct {
  PC_CompositeLink head;
  PCCompositeType  type;
  Vec              work1;
  Vec              work2;
  PetscScalar      alpha;
} PC_Composite;

static PetscErrorCode PCApply_Composite_Multiplicative(PC pc, Vec x, Vec y)
{
  PC_Composite    *jac  = (PC_Composite *)pc->data;
  PC_CompositeLink next = jac->head;
  Mat              mat  = pc->pmat;

  PetscFunctionBegin;
  PetscCheck(next, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "No composite preconditioners supplied via PCCompositeAddPCType() or -pc_composite_pcs");

  /* Set the reuse flag on children PCs */
  while (next) {
    PetscCall(PCSetReusePreconditioner(next->pc, pc->reusepreconditioner));
    next = next->next;
  }
  next = jac->head;

  if (next->next && !jac->work2) { /* allocate second work vector */
    PetscCall(VecDuplicate(jac->work1, &jac->work2));
  }
  if (pc->useAmat) mat = pc->mat;
  PetscCall(PCApply(next->pc, x, y)); /* y <- B x */
  while (next->next) {
    next = next->next;
    PetscCall(MatMult(mat, y, jac->work1));               /* work1 <- A y */
    PetscCall(VecWAXPY(jac->work2, -1.0, jac->work1, x)); /* work2 <- x - work1 */
    PetscCall(PCApply(next->pc, jac->work2, jac->work1)); /* work1 <- C work2 */
    PetscCall(VecAXPY(y, 1.0, jac->work1));               /* y <- y + work1 = B x + C (x - A B x) = (B + C (1 - A B)) x */
  }
  if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
    while (next->previous) {
      next = next->previous;
      PetscCall(MatMult(mat, y, jac->work1));
      PetscCall(VecWAXPY(jac->work2, -1.0, jac->work1, x));
      PetscCall(PCApply(next->pc, jac->work2, jac->work1));
      PetscCall(VecAXPY(y, 1.0, jac->work1));
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PCApplyTranspose_Composite_Multiplicative(PC pc, Vec x, Vec y)
{
  PC_Composite    *jac  = (PC_Composite *)pc->data;
  PC_CompositeLink next = jac->head;
  Mat              mat  = pc->pmat;

  PetscFunctionBegin;
  PetscCheck(next, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "No composite preconditioners supplied via PCCompositeAddPCType() or -pc_composite_pcs");
  if (next->next && !jac->work2) { /* allocate second work vector */
    PetscCall(VecDuplicate(jac->work1, &jac->work2));
  }
  if (pc->useAmat) mat = pc->mat;
  /* locate last PC */
  while (next->next) next = next->next;
  PetscCall(PCApplyTranspose(next->pc, x, y));
  while (next->previous) {
    next = next->previous;
    PetscCall(MatMultTranspose(mat, y, jac->work1));
    PetscCall(VecWAXPY(jac->work2, -1.0, jac->work1, x));
    PetscCall(PCApplyTranspose(next->pc, jac->work2, jac->work1));
    PetscCall(VecAXPY(y, 1.0, jac->work1));
  }
  if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
    next = jac->head;
    while (next->next) {
      next = next->next;
      PetscCall(MatMultTranspose(mat, y, jac->work1));
      PetscCall(VecWAXPY(jac->work2, -1.0, jac->work1, x));
      PetscCall(PCApplyTranspose(next->pc, jac->work2, jac->work1));
      PetscCall(VecAXPY(y, 1.0, jac->work1));
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
    This is very special for a matrix of the form alpha I + R + S
    where first preconditioner is built from alpha I + S and second from
    alpha I + R
*/
static PetscErrorCode PCApply_Composite_Special(PC pc, Vec x, Vec y)
{
  PC_Composite    *jac  = (PC_Composite *)pc->data;
  PC_CompositeLink next = jac->head;

  PetscFunctionBegin;
  PetscCheck(next, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "No composite preconditioners supplied via PCCompositeAddPCType() or -pc_composite_pcs");
  PetscCheck(next->next && !next->next->next, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Special composite preconditioners requires exactly two PCs");

  /* Set the reuse flag on children PCs */
  PetscCall(PCSetReusePreconditioner(next->pc, pc->reusepreconditioner));
  PetscCall(PCSetReusePreconditioner(next->next->pc, pc->reusepreconditioner));

  PetscCall(PCApply(next->pc, x, jac->work1));
  PetscCall(PCApply(next->next->pc, jac->work1, y));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PCApply_Composite_Additive(PC pc, Vec x, Vec y)
{
  PC_Composite    *jac  = (PC_Composite *)pc->data;
  PC_CompositeLink next = jac->head;

  PetscFunctionBegin;
  PetscCheck(next, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "No composite preconditioners supplied via PCCompositeAddPCType() or -pc_composite_pcs");

  /* Set the reuse flag on children PCs */
  while (next) {
    PetscCall(PCSetReusePreconditioner(next->pc, pc->reusepreconditioner));
    next = next->next;
  }
  next = jac->head;

  PetscCall(PCApply(next->pc, x, y));
  while (next->next) {
    next = next->next;
    PetscCall(PCApply(next->pc, x, jac->work1));
    PetscCall(VecAXPY(y, 1.0, jac->work1));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PCApplyTranspose_Composite_Additive(PC pc, Vec x, Vec y)
{
  PC_Composite    *jac  = (PC_Composite *)pc->data;
  PC_CompositeLink next = jac->head;

  PetscFunctionBegin;
  PetscCheck(next, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "No composite preconditioners supplied via PCCompositeAddPCType() or -pc_composite_pcs");
  PetscCall(PCApplyTranspose(next->pc, x, y));
  while (next->next) {
    next = next->next;
    PetscCall(PCApplyTranspose(next->pc, x, jac->work1));
    PetscCall(VecAXPY(y, 1.0, jac->work1));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PCSetUp_Composite(PC pc)
{
  PC_Composite    *jac  = (PC_Composite *)pc->data;
  PC_CompositeLink next = jac->head;
  DM               dm;

  PetscFunctionBegin;
  if (!jac->work1) PetscCall(MatCreateVecs(pc->pmat, &jac->work1, NULL));
  PetscCall(PCGetDM(pc, &dm));
  while (next) {
    if (!next->pc->dm) PetscCall(PCSetDM(next->pc, dm));
    if (!next->pc->mat) PetscCall(PCSetOperators(next->pc, pc->mat, pc->pmat));
    next = next->next;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PCSetUpOnBlocks_Composite(PC pc)
{
  PC_Composite    *jac  = (PC_Composite *)pc->data;
  PC_CompositeLink next = jac->head;
  PCFailedReason   reason;

  PetscFunctionBegin;
  while (next) {
    PetscCall(PCSetUp(next->pc));
    PetscCall(PCGetFailedReasonRank(next->pc, &reason));
    if (reason) pc->failedreason = reason;
    next = next->next;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PCReset_Composite(PC pc)
{
  PC_Composite    *jac  = (PC_Composite *)pc->data;
  PC_CompositeLink next = jac->head;

  PetscFunctionBegin;
  while (next) {
    PetscCall(PCReset(next->pc));
    next = next->next;
  }
  PetscCall(VecDestroy(&jac->work1));
  PetscCall(VecDestroy(&jac->work2));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PCDestroy_Composite(PC pc)
{
  PC_Composite    *jac  = (PC_Composite *)pc->data;
  PC_CompositeLink next = jac->head, next_tmp;

  PetscFunctionBegin;
  PetscCall(PCReset_Composite(pc));
  while (next) {
    PetscCall(PCDestroy(&next->pc));
    next_tmp = next;
    next     = next->next;
    PetscCall(PetscFree(next_tmp));
  }
  PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCCompositeSetType_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCCompositeGetType_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCCompositeAddPCType_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCCompositeAddPC_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCCompositeGetNumberPC_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCCompositeGetPC_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCCompositeSpecialSetAlpha_C", NULL));
  PetscCall(PetscFree(pc->data));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PCSetFromOptions_Composite(PC pc, PetscOptionItems *PetscOptionsObject)
{
  PC_Composite    *jac  = (PC_Composite *)pc->data;
  PetscInt         nmax = 8, i;
  PC_CompositeLink next;
  char            *pcs[8];
  PetscBool        flg;

  PetscFunctionBegin;
  PetscOptionsHeadBegin(PetscOptionsObject, "Composite preconditioner options");
  PetscCall(PetscOptionsEnum("-pc_composite_type", "Type of composition", "PCCompositeSetType", PCCompositeTypes, (PetscEnum)jac->type, (PetscEnum *)&jac->type, &flg));
  if (flg) PetscCall(PCCompositeSetType(pc, jac->type));
  PetscCall(PetscOptionsStringArray("-pc_composite_pcs", "List of composite solvers", "PCCompositeAddPCType", pcs, &nmax, &flg));
  if (flg) {
    for (i = 0; i < nmax; i++) {
      PetscCall(PCCompositeAddPCType(pc, pcs[i]));
      PetscCall(PetscFree(pcs[i])); /* deallocate string pcs[i], which is allocated in PetscOptionsStringArray() */
    }
  }
  PetscOptionsHeadEnd();

  next = jac->head;
  while (next) {
    PetscCall(PCSetFromOptions(next->pc));
    next = next->next;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PCView_Composite(PC pc, PetscViewer viewer)
{
  PC_Composite    *jac  = (PC_Composite *)pc->data;
  PC_CompositeLink next = jac->head;
  PetscBool        iascii;

  PetscFunctionBegin;
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
  if (iascii) {
    PetscCall(PetscViewerASCIIPrintf(viewer, "Composite PC type - %s\n", PCCompositeTypes[jac->type]));
    PetscCall(PetscViewerASCIIPrintf(viewer, "PCs on composite preconditioner follow\n"));
    PetscCall(PetscViewerASCIIPrintf(viewer, "---------------------------------\n"));
  }
  if (iascii) PetscCall(PetscViewerASCIIPushTab(viewer));
  while (next) {
    PetscCall(PCView(next->pc, viewer));
    next = next->next;
  }
  if (iascii) {
    PetscCall(PetscViewerASCIIPopTab(viewer));
    PetscCall(PetscViewerASCIIPrintf(viewer, "---------------------------------\n"));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PCCompositeSpecialSetAlpha_Composite(PC pc, PetscScalar alpha)
{
  PC_Composite *jac = (PC_Composite *)pc->data;

  PetscFunctionBegin;
  jac->alpha = alpha;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PCCompositeSetType_Composite(PC pc, PCCompositeType type)
{
  PC_Composite *jac = (PC_Composite *)pc->data;

  PetscFunctionBegin;
  if (type == PC_COMPOSITE_ADDITIVE) {
    pc->ops->apply          = PCApply_Composite_Additive;
    pc->ops->applytranspose = PCApplyTranspose_Composite_Additive;
  } else if (type == PC_COMPOSITE_MULTIPLICATIVE || type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
    pc->ops->apply          = PCApply_Composite_Multiplicative;
    pc->ops->applytranspose = PCApplyTranspose_Composite_Multiplicative;
  } else if (type == PC_COMPOSITE_SPECIAL) {
    pc->ops->apply          = PCApply_Composite_Special;
    pc->ops->applytranspose = NULL;
  } else SETERRQ(PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "Unknown composite preconditioner type");
  jac->type = type;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PCCompositeGetType_Composite(PC pc, PCCompositeType *type)
{
  PC_Composite *jac = (PC_Composite *)pc->data;

  PetscFunctionBegin;
  *type = jac->type;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PCCompositeAddPC_Composite(PC pc, PC subpc)
{
  PC_Composite    *jac;
  PC_CompositeLink next, ilink;
  PetscInt         cnt = 0;
  const char      *prefix;
  char             newprefix[20];

  PetscFunctionBegin;
  PetscCall(PetscNew(&ilink));
  ilink->next = NULL;
  ilink->pc   = subpc;

  jac  = (PC_Composite *)pc->data;
  next = jac->head;
  if (!next) {
    jac->head       = ilink;
    ilink->previous = NULL;
  } else {
    cnt++;
    while (next->next) {
      next = next->next;
      cnt++;
    }
    next->next      = ilink;
    ilink->previous = next;
  }
  PetscCall(PCGetOptionsPrefix(pc, &prefix));
  PetscCall(PCSetOptionsPrefix(subpc, prefix));
  PetscCall(PetscSNPrintf(newprefix, 20, "sub_%d_", (int)cnt));
  PetscCall(PCAppendOptionsPrefix(subpc, newprefix));
  PetscCall(PetscObjectReference((PetscObject)subpc));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PCCompositeAddPCType_Composite(PC pc, PCType type)
{
  PC subpc;

  PetscFunctionBegin;
  PetscCall(PCCreate(PetscObjectComm((PetscObject)pc), &subpc));
  PetscCall(PetscObjectIncrementTabLevel((PetscObject)subpc, (PetscObject)pc, 1));
  PetscCall(PCCompositeAddPC_Composite(pc, subpc));
  /* type is set after prefix, because some methods may modify prefix, e.g. pcksp */
  PetscCall(PCSetType(subpc, type));
  PetscCall(PCDestroy(&subpc));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PCCompositeGetNumberPC_Composite(PC pc, PetscInt *n)
{
  PC_Composite    *jac;
  PC_CompositeLink next;

  PetscFunctionBegin;
  jac  = (PC_Composite *)pc->data;
  next = jac->head;
  *n   = 0;
  while (next) {
    next = next->next;
    (*n)++;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PCCompositeGetPC_Composite(PC pc, PetscInt n, PC *subpc)
{
  PC_Composite    *jac;
  PC_CompositeLink next;
  PetscInt         i;

  PetscFunctionBegin;
  jac  = (PC_Composite *)pc->data;
  next = jac->head;
  for (i = 0; i < n; i++) {
    PetscCheck(next->next, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_INCOMP, "Not enough PCs in composite preconditioner");
    next = next->next;
  }
  *subpc = next->pc;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PCCompositeSetType - Sets the type of composite preconditioner.

  Logically Collective

  Input Parameters:
+ pc   - the preconditioner context
- type - `PC_COMPOSITE_ADDITIVE` (default), `PC_COMPOSITE_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`

  Options Database Key:
. -pc_composite_type <type: one of multiplicative, additive, special> - Sets composite preconditioner type

  Level: advanced

.seealso: [](ch_ksp), `PCCOMPOSITE`, `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PCCompositeType`,
          `PCCompositeGetType()`
@*/
PetscErrorCode PCCompositeSetType(PC pc, PCCompositeType type)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscValidLogicalCollectiveEnum(pc, type, 2);
  PetscTryMethod(pc, "PCCompositeSetType_C", (PC, PCCompositeType), (pc, type));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PCCompositeGetType - Gets the type of composite preconditioner.

  Logically Collective

  Input Parameter:
. pc - the preconditioner context

  Output Parameter:
. type - `PC_COMPOSITE_ADDITIVE` (default), `PC_COMPOSITE_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`

  Level: advanced

.seealso: [](ch_ksp), `PCCOMPOSITE`, `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PCCompositeType`,
          `PCCompositeSetType()`
@*/
PetscErrorCode PCCompositeGetType(PC pc, PCCompositeType *type)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscUseMethod(pc, "PCCompositeGetType_C", (PC, PCCompositeType *), (pc, type));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PCCompositeSpecialSetAlpha - Sets alpha for the special composite preconditioner, `PC_COMPOSITE_SPECIAL`,
  for $\alpha I + R + S$

  Logically Collective

  Input Parameters:
+ pc    - the preconditioner context
- alpha - scale on identity

  Level: developer

.seealso: [](ch_ksp), `PCCOMPOSITE`, `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PCCompositeType`,
          `PCCompositeSetType()`, `PCCompositeGetType()`
@*/
PetscErrorCode PCCompositeSpecialSetAlpha(PC pc, PetscScalar alpha)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscValidLogicalCollectiveScalar(pc, alpha, 2);
  PetscTryMethod(pc, "PCCompositeSpecialSetAlpha_C", (PC, PetscScalar), (pc, alpha));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PCCompositeAddPCType - Adds another `PC` of the given type to the composite `PC`.

  Collective

  Input Parameters:
+ pc   - the preconditioner context
- type - the type of the new preconditioner

  Level: intermediate

.seealso: [](ch_ksp), `PCCOMPOSITE`, `PCCompositeAddPC()`, `PCCompositeGetNumberPC()`
@*/
PetscErrorCode PCCompositeAddPCType(PC pc, PCType type)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscTryMethod(pc, "PCCompositeAddPCType_C", (PC, PCType), (pc, type));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PCCompositeAddPC - Adds another `PC` to the composite `PC`.

  Collective

  Input Parameters:
+ pc    - the preconditioner context
- subpc - the new preconditioner

  Level: intermediate

.seealso: [](ch_ksp), `PCCOMPOSITE`, `PCCompositeAddPCType()`, `PCCompositeGetNumberPC()`
@*/
PetscErrorCode PCCompositeAddPC(PC pc, PC subpc)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscValidHeaderSpecific(subpc, PC_CLASSID, 2);
  PetscTryMethod(pc, "PCCompositeAddPC_C", (PC, PC), (pc, subpc));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PCCompositeGetNumberPC - Gets the number of `PC` objects in the composite `PC`.

  Not Collective

  Input Parameter:
. pc - the preconditioner context

  Output Parameter:
. num - the number of sub pcs

  Level: developer

.seealso: [](ch_ksp), `PCCOMPOSITE`, `PCCompositeGetPC()`, `PCCompositeAddPC()`, `PCCompositeAddPCType()`
@*/
PetscErrorCode PCCompositeGetNumberPC(PC pc, PetscInt *num)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscAssertPointer(num, 2);
  PetscUseMethod(pc, "PCCompositeGetNumberPC_C", (PC, PetscInt *), (pc, num));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PCCompositeGetPC - Gets one of the `PC` objects in the composite `PC`.

  Not Collective

  Input Parameters:
+ pc - the preconditioner context
- n  - the number of the pc requested

  Output Parameter:
. subpc - the PC requested

  Level: intermediate

  Note:
  To use a different operator to construct one of the inner preconditioners first call `PCCompositeGetPC()`, then
  call `PCSetOperators()` on that `PC`.

.seealso: [](ch_ksp), `PCCOMPOSITE`, `PCCompositeAddPCType()`, `PCCompositeGetNumberPC()`, `PCSetOperators()`
@*/
PetscErrorCode PCCompositeGetPC(PC pc, PetscInt n, PC *subpc)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscAssertPointer(subpc, 3);
  PetscUseMethod(pc, "PCCompositeGetPC_C", (PC, PetscInt, PC *), (pc, n, subpc));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*MC
     PCCOMPOSITE - Build a preconditioner by composing together several preconditioners

   Options Database Keys:
+  -pc_composite_type <type: one of multiplicative, additive, symmetric_multiplicative, special> - Sets composite preconditioner type
.  -pc_use_amat                                                                                  - activates `PCSetUseAmat()`
-  -pc_composite_pcs                                                                             - <pc0,pc1,...> list of PCs to compose

   Level: intermediate

   Notes:
   To use a Krylov method inside the composite preconditioner, set the `PCType` of one or more
   inner `PC`s to be `PCKSP`. Using a Krylov method inside another Krylov method can be dangerous (you get divergence or
   the incorrect answer) unless you use `KSPFGMRES` as the outer Krylov method

   To use a different operator to construct one of the inner preconditioners first call `PCCompositeGetPC()`, then
   call `PCSetOperators()` on that `PC`.

.seealso: [](ch_ksp), `PCCreate()`, `PCSetType()`, `PCType`, `PC`,
          `PCSHELL`, `PCKSP`, `PCCompositeSetType()`, `PCCompositeSpecialSetAlpha()`, `PCCompositeAddPCType()`,
          `PCCompositeGetPC()`, `PCSetUseAmat()`, `PCCompositeAddPC()`, `PCCompositeGetNumberPC()`
M*/

PETSC_EXTERN PetscErrorCode PCCreate_Composite(PC pc)
{
  PC_Composite *jac;

  PetscFunctionBegin;
  PetscCall(PetscNew(&jac));

  pc->ops->apply           = PCApply_Composite_Additive;
  pc->ops->applytranspose  = PCApplyTranspose_Composite_Additive;
  pc->ops->setup           = PCSetUp_Composite;
  pc->ops->setuponblocks   = PCSetUpOnBlocks_Composite;
  pc->ops->reset           = PCReset_Composite;
  pc->ops->destroy         = PCDestroy_Composite;
  pc->ops->setfromoptions  = PCSetFromOptions_Composite;
  pc->ops->view            = PCView_Composite;
  pc->ops->applyrichardson = NULL;

  pc->data   = (void *)jac;
  jac->type  = PC_COMPOSITE_ADDITIVE;
  jac->work1 = NULL;
  jac->work2 = NULL;
  jac->head  = NULL;

  PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCCompositeSetType_C", PCCompositeSetType_Composite));
  PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCCompositeGetType_C", PCCompositeGetType_Composite));
  PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCCompositeAddPCType_C", PCCompositeAddPCType_Composite));
  PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCCompositeAddPC_C", PCCompositeAddPC_Composite));
  PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCCompositeGetNumberPC_C", PCCompositeGetNumberPC_Composite));
  PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCCompositeGetPC_C", PCCompositeGetPC_Composite));
  PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCCompositeSpecialSetAlpha_C", PCCompositeSpecialSetAlpha_Composite));
  PetscFunctionReturn(PETSC_SUCCESS);
}